LESSON PLAN

MATHEMATICS:

SUPERHERO COMBINATIONS

STAGE THREE

Unit/Lesson Title – Superhero Combinations Stage - Three Year - SixAim for the lesson:To allow students to investigate and practice different methods of problem solving to solve a mathematical problem with multiple combinations/solutions. Students will be able to develop and apply problem solving strategies and mathematical reasoning skills. Students will also be required to justify and reflect on their preferred method of calculation.

Syllabus Outcomes MA3-1WM – describes and represents mathematical situations in a variety of

ways using mathematical terminology and some conventions MA3-2WM – selects and applies appropriate problem-solving strategies,

including the use of digital technologies, in undertaking investigations MA3-3WM – gives a valid reason for supporting one possible solution over

another MA3-5NA – selects and applies appropriate strategies for addition and

subtraction with counting numbers of any sizePrior KnowledgeStudents should be able to add and subtract large whole numbers including three and four digit numbers.

Resources Superhero handout with points allocated to each character (appendix one) A4 pages with values of each character (appendix two) Paper counters with values of each character (appendix three) Pens/pencils Paper Calculator (if required)

Learning Experiences (include details about class-organisation and teaching strategies, where relevant)Introduction (Engagement)

Introduce the concept of superheroes and how in comics/movies/video games a group of superheroes will combine their strengths and work together to defeat the villain. Pose questions to capture the attention of the students and engage them in the activity. Who wants to be a superhero? Which superpower would you have? Why do you think superheroes work as a team?

Supply the students with a handout with pictures of a group of superheroes and a single villain, with a numerical value applied to each to represent their strength. In this example, the superheroes are characters from Marvel’s The Avengers and the villain is Ultron. Pose the following scenario to the students:

The Avengers need to work together to stop Ultron from destroying the world. Ultron has a strength of 2000 points. How many different combinations of Avengers can be used to defeat Ultron? Each Avenger can only be used once. Students are also required to make combinations using the least number of Avengers possible. For example, the strengths of all of the Avengers results in a sum of 3675 points, however only 2000 points are required to defeat Ultron, meaning some members of the Avengers are unnecessary.

Discuss the purpose of the activity with the students. Why is it important that we know more than one way to do something? Ensure that all students understand the problem and what is being asked of them. What do we need to do? What are the rules?

Assessment

Ask students to identify different methods of problem solving (guess and check, tree diagram, table, etc)

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EXTENSION ACTIVITYStudents who complete the task quickly will be posed an additional problem: Thor has been injured in the battle and now has a strength of only 500 points. Are the Avengers still able to defeat Ultron? If yes, how many different combinations of Avengers can do this?Body(Exploration/Transformation/Presentation)

Begin the practical application by demonstrating how multiple items can be combined to equal the value of a single item. An example that could be used is by drawing a set of scales on the interactive whiteboard and displaying how three cars equals the weight of one elephant. Another example that could be used is by using pictures of money that illustrate how five $20 notes equals one $100 note. Ask students to explain why these items are of equal/the same value. Is this (one side) the same as this (other side)?

Move on to the superhero problem. Select some students to stand in front of the class holding the A4 sheets (appendix two) to represent the individual characters. Work with the class to find one or two combinations and display these on the interactive whiteboard. Use this opportunity to clarify the criteria of the problem and ask the students to state why these combinations do or do not answer the question. Does the combination use the minimum number of characters? Does the total of the heroes combined strength equal the strength of Ultron? Discuss other possible methods of solving the problem such as using a table or making a guess and check list. What are some other ways we could find combinations? Is there anything we can do to make it less likely that we will use the same combination but just in a different order?

Ask students to return to their desks. Supply students with handout (appendix one). Working in pairs, students will need to use their mathematical (addition and subtraction) and problem solving skills to try to find as many combinations as possible. Students will be encouraged to use whichever method they choose from those introduced earlier in the lesson or another method of their choice. Students can choose to use the paper counters (appendix three) to assist them in their calculations

Observe Collect work

samples from students

Conclusion (Presentation/Reflection)

At the conclusion of the lesson, ask students to compare their answers and discuss and demonstrate the method used to calculate those answers. Students will then be asked to review and reflect on the method they used and determine if this was the best method. Students will be required to justify their answer. What methods did you use? Do you think your method was best? If you did the problem again would you do it the same way?

Conclude by summarising the different problem solving strategies learnt throughout the lesson. What are the different methods? Could we use these methods to complete other problems? If yes, what type of problems? Ask students to complete a written review of the activity in their books including:

What they learnt What they did/didn’t enjoy about the activity What they would do differently next time

Collect work samples

Verbal and written feedback from students

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SOLUTIONS

When keeping to the criteria of the problem, ten solutions can be found from the original problem. Eight combinations can be found to answer the extension activity. The different combinations and the characters used in these combinations is detailed below.

ORIGINAL PROBLEM

HU

LK

THO

R

IRO

N M

AN

CA

PTA

IN

AM

ERIC

A

BLA

CK

WID

OW

HA

WK

EYE

TOTA

L

SOLUTION 1 ✔ ✔ ✔ 2150

SOLUTION 2 ✔ ✔ ✔ 2100

SOLUTION 3 ✔ ✔ ✔ ✔ 2425

SOLUTION 4 ✔ ✔ ✔ 2050

SOLUTION 5 ✔ ✔ ✔ ✔ 2375

SOLUTION 6 ✔ ✔ ✔ ✔ 2325

SOLUTION 7 ✔ ✔ ✔ ✔ 2425

SOLUTION 8 ✔ ✔ ✔ ✔ 2400

SOLUTION 9 ✔ ✔ ✔ ✔ 2225

SOLUTION 10 ✔ ✔ ✔ ✔ 2175

EXTENSION ACTIVITY

HU

LK

THO

R

IRO

N M

AN

CA

PTA

IN

AM

ERIC

A

BLA

CK

WID

OW

HA

WK

EYE

TOTA

L

SOLUTION 1 ✔ ✔ ✔ 2050

SOLUTION 2 ✔ ✔ ✔ ✔ 2225

SOLUTION 3 ✔ ✔ ✔ ✔ 2200

SOLUTION 4 ✔ ✔ ✔ ✔ 2175

SOLUTION 5 ✔ ✔ ✔ ✔ 2150

SOLUTION 6 ✔ ✔ ✔ ✔ 2025

SOLUTION 7 ✔ ✔ ✔ ✔ 2025

SOLUTION 8 ✔ ✔ ✔ ✔ 2000

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APPENDIX ONE – SUPERHERO HANDOUT

HAWKEYE450 POINTS

HULK800 POINTS

ULTRON2000 POINTS

BLACK WIDOW475 POINTS

CAPTAIN AMERICA600 POINTS

IRON MAN650 POINTS

THOR700 POINTS

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APPENDIX TWO

APPENDIX THREE – PAPER COUNTERS

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HULK800 POINTS

CAPTAIN AMERICA

600 POINTS IRON MAN

650 POINTS

THOR

700 POINTS